Question: Find the greatest common factor of $8, 18,$ and $70$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of $8, 18,$ and $70$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}8 &=2\cdot2\cdot2\\\\\\\\ 18&=2\cdot3\cdot3\\\\\\\\ 70&=2\cdot5\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}8 &=2\cdot2\cdot2\\\\\\\\ 18&=2\cdot3\cdot3\\\\\\\\ 70&=2\cdot5\cdot7 \end{aligned}$ Each number shares the factor ${2},$ so the GCF is ${2}$. The greatest common factor of $8, 18,$ and $70$ is $2$.